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Circular Lorentz-Gauss beams

Yiqing Xu and Guoquan Zhou

Doc ID: 351175 Received 06 Nov 2018; Accepted 12 Dec 2018; Posted 13 Dec 2018  View: PDF

Abstract: A circular Lorentz-Gauss beam is introduced. The analytical optical field of the circular Lorentz-Gauss beam passingthrough a paraxial ABCD optical system is derived. Based on the second-order and the higher-order moments of the lightintensity, the analytical beam propagation factor of a circular Lorentz-Gauss beam and the analytical kurtosis parameter of acircular Lorentz-Gauss beam passing through a paraxial ABCD optical system have also been derived. The properties of thecircular Lorentz-Gauss beam propagating in free space are demonstrated. The normalized intensity distribution, the beamhalf width, the beam waist, the divergence, the beam propagation factor, and the kurtosis parameter of the circular Lorentz-Gauss beam are compared with those of the corresponding Lorentz-Gauss beam, respectively. The main difference betweenthe circular Lorentz-Gauss and the Lorentz-Gauss beams is their different periphery. The circular Lorentz-Gauss beam hasbetter symmetry than the Lorentz-Gauss beam. The beam propagation factor of the circular Lorentz-Gauss beam is alwaysslightly larger than that of the Lorentz-Gauss beam. Therefore, the circular Lorentz-Gauss beam is the enrichment andsupplementary of the existing Lorentz-Gauss beam.

Super-resolution algorithm based on Richardson-Lucydeconvolution for three-dimensional structuredillumination microscopy

Yanwei Zhang, Song Lang, Hongwei Wang, Jiasheng Liao, and Yan Gong

Doc ID: 314087 Received 28 Jun 2018; Accepted 11 Dec 2018; Posted 11 Dec 2018  View: PDF

Abstract: Three-dimensional structured illumination microscopy (3D-SIM) is a wide field super-resolution technique influorescent imaging that can double the resolution beyond its classical limit. We introduce a new threedimensionalreconstruction algorithm based on Richardson-Lucy deconvolution. The 3D-SIM imaging principle andthe reconstruction steps are demonstrated in detail. Microspheres and biological specimen are used to present theperformance of this method. The background of out-of-focus portion is effectively suppressed and true opticalsectioning and super resolution can be achieved simultaneously. For the custom-built 3D-SIM and thisreconstruction algorithm, the measured resolution was 99.5±5 nm laterally and 294±9 nm axially.

Assessment of plenoptic imaging for reconstruction of3D discrete and continuous luminous fields

Hecong Liu, Qianlong Wang, and Weiwei Cai

Doc ID: 347680 Received 09 Oct 2018; Accepted 11 Dec 2018; Posted 11 Dec 2018  View: PDF

Abstract: Volumetric tomography has become an indispensable tool for flow diagnostics. However, it usually suffers fromhigh experimental costs as multiple cameras are required in a typical tomographic system. Plenoptic imaging (PI)is a promising alternative which can simultaneously record spatial and angular information using only one singlecamera. Although PI has been pioneered by a few groups for 3D flow imaging, this particular application is still atits early stage of development and there are some aspects which need further investigation. In this work, we willsystematically assess three representative tomographic algorithms for PI via numerical studies. In addition, weshow here how 3D PI inversion can be interpreted from a tomographic perspective and how to convenientlyperform the calibration with an existing well-established method which can take into account the effect of lensdistortion. A proof-of-concept experiment was also conducted and the conclusions drawn were consistent withthose from numerical studies. Although this work was discussed under the context of flow/flame imaging, thegeneral conclusions is also applicable to other application fields such biomedical imaging.

Determining ellipses from low resolution images with a comprehensive image formation model

Zygmunt Szpak and Wojciech Chojnacki

Doc ID: 337832 Received 11 Jul 2018; Accepted 04 Dec 2018; Posted 05 Dec 2018  View: PDF

Abstract: When determining the parameters of a parametric planar shape based on a single low-resolution image, common estimation paradigms lead to inaccurate parameter estimates. The reason behind poor estimation results is that standard estimation frameworks fail to model the image formation process at a sufficiently detailed level of analysis. We propose a new method for estimating the parameters of a planar elliptic shape based on a single photon-limited, low-resolution image. Our technique incorporates the effects of several elements---the point-spread function, the discretisation step, the quantisation step and photon noise---into a single cohesive and manageable statistical model. While we concentrate on the particular task of estimating the parameters of elliptic shapes, our ideas and methods have a much broader scope and can be used to address the problem of estimating the parameters of an arbitrary parametrically representable planar shape. Comprehensive experimental results on simulated and real imagery demonstrate that our approach yields parameter estimates with unprecedented accuracy. Furthermore, our method supplies a parameter covariance matrix as a measure of uncertainty for the estimated parameters, as well as a planar confidence region as a means for visualising the parameter uncertainty. The mathematical model developed in this paper may prove useful in a variety of disciplines which operate with imagery at the limits of resolution.

A comparative study of multi-look processing for phase map de-noising in digital Fresnel holographic interferometry

Silvio Montresor, Pasquale Memmolo, Vittorio Bianco, Pietro Ferraro, and Pascal Picart

Doc ID: 347525 Received 04 Oct 2018; Accepted 04 Dec 2018; Posted 05 Dec 2018  View: PDF

Abstract: This paper presents a comparative study of multi-look approaches for de-noising phase maps from digital holographic interferometry. A database of 160 simulated phase fringe patterns with 8 different phase fringe patterns with fringe diversity was computed. For each fringe pattern, 20 realistic noise realizations are generated in order to simulate a multi-look process with 20 inputs. A set of 22 de-noising algorithms were selected and processed for each simulation. Three approaches for multi-look processing are evaluated. Quantitative appraisal is obtained using two metrics. Results show good agreement for algorithm rankings obtained with both two metrics. One singular and highly practical result of the study is that multi-look approach with averaging of looks before noise processing performs better than averaging computed with all de-noised looks. The results also demonstrate that the two-dimensional windowed Fourier transform filtering exhibits the best performance in all cases, and that the BM3D algorithm is at the second place in the ranking.

Research on hole filling algorithm of pointcloud based on structure from motion

Shaoyan Gai, Feipeng Da, LULU ZENG, and YUAN HUANG

Doc ID: 345548 Received 10 Sep 2018; Accepted 03 Dec 2018; Posted 03 Dec 2018  View: PDF

Abstract: Point cloud can be obtained from 3D-mearsurement reconstruction based on fringeprojection. However, there are holes in point cloud due to complicated shaped objects and thedefect of the method. The holes have a profound impact on the following data processing. Afitting approach to fill the holes based on structure from motion (SFM) is proposed in thispaper. Firstly, fringe projection with two-dimensional phase is used to extract the holeboundary. Secondly, registration of the SFM point cloud and fringe projection point cloud arecarried out. Then supplementary points are extracted. Thirdly, the holes are filled based onradial basis function (RBF) on point cloud added with supplementary points. This method hasbeen proven to be robust by experiments, and information of complex surface holes can berestored sufficiently.

Self-reference hyperspectral holographic microscopy

Georgy Kalenkov, Sergey Kalenkov, and Alexander Shtanko

Doc ID: 345752 Received 17 Sep 2018; Accepted 29 Nov 2018; Posted 30 Nov 2018  View: PDF

Abstract: Self-reference hyperspectral holographic microscopy with an extended, spatially incoherent, polychromaticsource is suggested and experimentally verified. The reference field is the zero order Fourier componentof the object filtered out by a ring-shaped mask placed in the Fourier plane of the optical system.A set of spectrally-resolved complex amplitudes of the object is obtained on the basis of the standardmicroscope, equipped with a Michelson interferometer. Experiments on registration of hyperspectralholograms confirming validity of the proposed theoretical model are carried out.

Volume holographic spatial-spectral imagingsystems

Sunil Vyas, Yu-Hsin Chia, and Yuan Luo

Doc ID: 347288 Received 01 Oct 2018; Accepted 29 Nov 2018; Posted 30 Nov 2018  View: PDF

Abstract: In this article, we present an overview of the recent developments in applicationof volume holographic imaging techniques in microscopy. In these techniques, threedimensionalimaging incorporates multiplexed volume holographic gratings, which areformed in PQ-PMMA photopolymer and act as spatial-spectral filters, to obtain multi-planeimages from a volumetric object, without scanning. We introduce recent major roles ofvolume holography in different imaging modalities, including large-capacity spatial-spectralmulti-plane microscopy, digital holographic microscopy, and structured Talbot (or speckle)illumination fluorescence imaging. Among various imaging applications of volumeholography, simultaneous multi-plane fluorescence microscopy for collecting spatial-spectralinformation is distinct and has great potentials for hyperspectral imaging. Depth selectivespatial-spectral information from an object are particularly useful for designing highresolution microscope in real-time operation. We further discuss volume holography inparticle trapping and beam shaping. In addition, we investigate future prospects of volumeholography in microscopy, as well as endoscopy.

Influence of the description of the scattering matrix onthe permittivity reconstruction with a quantitativeimaging procedure: polarization effects

Christelle Eyraud, Hassan Saleh, and Jean-Michel Geffrin

Doc ID: 340286 Received 30 Jul 2018; Accepted 29 Nov 2018; Posted 30 Nov 2018  View: PDF

Abstract: This paper focuses on the role of polarization - and more specifically, the effect of its selection - in 3Dquantitative imaging obtained from scattered field measurements. Although polarization is now commonlyused in linear imaging procedures (when unknowns are linked by a linear relationship to themeasured signal), the influence of polarization choice is generally ignored in non-linear imaging problems.In this paper, we propose a formulation to obtain the 3D permittivity map, by a non-linear imagingprocedure, from the scattering matrix. This allows, from the same data set, to select the desired polarizationcase as input data for the imaging algorithm. We present a study of the influence of the input datapolarization choice on the reconstructed permittivity map. This work shows that a suitable basis choicefor the description of the scattering matrix and an appropriate selection of the element of this scatteringmatrix can greatly improve imaging results.

Nonparaxial propagation of vector vortexbeams diffracted by a circular aperture

Xianghan Cui, Chaolin Wang, and Xinting Jia

Doc ID: 345618 Received 11 Sep 2018; Accepted 27 Nov 2018; Posted 30 Nov 2018  View: PDF

Abstract: In terms of the vectorial Rayleigh-Sommerfeld diffraction integral, the analyticalexpressions of the arbitrary vector vortex Laguerre-Gaussian beams on the higher-orderPoincaré sphere diffracted by a circular aperture propagating in the nonparaxial and paraxialregimes are presented. The cylindrical vector beam, circularly polarized vortex beam, andelliptically polarized vortex beam are viewed as the special cases of our general result. Theanalyses show that the nonparaxial evolution properties of the apertured vector vortex beamsare determined by the waist width, the truncation parameter, the topological charge, and theellipticity angle.

Spherical sampling methods for the calculationof metamer mismatch volumes.

Michal Mackiewicz, Hans Jakobs Rivertz, and Graham Finlayson

Doc ID: 340864 Received 30 Jul 2018; Accepted 27 Nov 2018; Posted 28 Nov 2018  View: PDF

Abstract: In this article, we propose two methods of calculating a theoretically maximal metamermismatch volumes. Unlike prior art techniques, our methods do not make any assumptions onthe shape of spectra on the boundary of the mismatch volumes. Both methods utilise a sphericalsampling approach, but they calculate mismatch volumes in two different ways. The first methoduses a linear programming optimisation, while the second is a computational geometry approachbased on half-space intersection. We show that under certain conditions the theoretically maximalmetamer mismatch volume is significantly larger than the one approximated using prior artmethod.

Extension of the span and optimization of the optical “magiccarpet”: generation of a wide quasi-non-diffracting light sheet

Mouna Haouas, Brahim Chebbi, and Ilya Golub

Doc ID: 341125 Received 07 Aug 2018; Accepted 27 Nov 2018; Posted 28 Nov 2018  View: PDF

Abstract: Light sheet illumination is the basis in developing light sheet microscopy (LSM), a technique with significant advantages compared toother classical techniques. Most proposed optical systems to generate the light sheet for LSM use many optical elements, whichrequire extensive adjustments and are costly; moreover, they generate non-uniform or semi-uniform light sheet or have a short depthof field (DOF). A simple scheme using a pair of double slits and a cylindrical lens for generating a quasi-non-diffracting 2D lightsheet was reported in Ref. [1]. In the present investigation, we elaborate on the optimization of the mask used. As the separationbetween the two slits increases, the light sheet becomes thinner and the DOF smaller and vice versa. The slits’ width does not affectthe light sheet thickness, but affects the intensity of the side lobes. For convergence angles of the inner slits from 0.75o to 8o, anoptimum ratio of the slits separation/width of 2.182 is recommended. The obtained light sheet is quasi-diffraction free, namely whileits DOF is comparable to that of a Gaussian beam, its diffraction broadening is substantially smaller.We also add to the previously developed configuration a Powell lens in order to expand the beam in the span-wise direction whilekeeping a nearly constant intensity in this dimension. We perform scalar diffraction theory calculations and conduct measurementsshowing the nearly constant intensity in the significantly broadened span of the light sheet. Potential applications for the augmentedwidth include imaging of certain large embryos, laser micromachining and micro particle image velocimetry.

Anisotropic linear media: Opto-mechanicalanalogies between discontinuity surfaces

Consuelo Bellver-Cebreros and Marcelo Rodríguez-Danta

Doc ID: 341146 Received 30 Jul 2018; Accepted 27 Nov 2018; Posted 28 Nov 2018  View: PDF

Abstract: Opto-mechanical analogies have been derived by casting electromagnetic fieldconservation laws for linear anisotropic media as balance equations of continuous mechanics,starting only and exclusively from Maxwell equations. Focusing on the asymmetry ofMaxwell stress tensor T , electromagnetic couple density C is obtained in terms of theantisymmetric part of T , by using an equivalent system of forces. By considering a wavefront as a discontinuity surface, analogies with impulsive dynamics and the double layermodel for anisotropic media have been suggested. The procedure is applied to impedancematched metamaterials and the eikonal equation for these media is reobtained.

Diffraction limited superresolution ptychography in theRayleigh Sommerfeld regime

Daniel Claus and John Rodenburg

Doc ID: 342844 Received 21 Aug 2018; Accepted 27 Nov 2018; Posted 28 Nov 2018  View: PDF

Abstract: Superresolution in lensless near field ptychography is demonstrated via the application of a stronglycurved illumination function. The reconstruction is performed using the Rayleigh-Sommerfeld diffractionintegral, which is implemented via a pixel-size adjustable angular spectrum method. In this mannerthe reconstructed object details, which are not only smaller than the pixel-size of the sensor but evensmaller than the smallest resolvable object detail defined by the effective NA of the 2D sensor, is enabled.The expected resolution, as predicted by the angles of scatter present in the optical configuration, is experimentallyvalidated using a US air force resolution test target. The approach discussed here is not onlylimited to ptychography, but can be extended to other coherent diffractive imaging modalities such asobject scanning holography or optical diffraction tomography, so as to enable high resolution near fieldquantitative phase imaging.

Orbital angular momentum of an elliptic beamafter an elliptic spiral phase plate

Alexey Kovalev and Victor Kotlyar

Doc ID: 345962 Received 14 Sep 2018; Accepted 27 Nov 2018; Posted 28 Nov 2018  View: PDF

Abstract: We obtain a simple closed expression for the normalized orbital angularmomentum (OAM) (OAM per unit power) of an arbitrary paraxial light beam with an ellipticshape, diffracted by an elliptic spiral phase plate (SPP), rotated by an arbitrary angle aroundthe optical axis. At this, ellipticities of the beam and of the SPP can be different. It is shownthat when an elliptic beam illuminates an elliptic SPP, the normalized OAM of the outputbeam is maximal (minimal) when both the beam and the SPP are oriented in the same(orthogonal) directions. The results can be used in optical trapping, e.g. for continuous changeof the OAM transferred to a particle by rotating the SPP around the optical axis.

Imaging through distributed-volume aberrations using single-shot digital holography

Casey Pellizzari, Mark Spencer, and Charles Bouman

Doc ID: 346294 Received 21 Sep 2018; Accepted 27 Nov 2018; Posted 28 Nov 2018  View: PDF

Abstract: This paper explores the use of single-shot digital holography data and a novel algorithm, referred to as multi-plane iterative reconstruction (MIR), for imaging through distributed-volume aberrations. Such aberrations result in a linear, shift-varying or “anisoplanatic” physical process, where multiple look angles give rise to different point-spread functions within the field of view of the imaging system. The MIR algorithm jointly computes the maximum a posteriori estimates of the anisoplanatic phase errors and the speckle-free object reflectance from the single-shot digital holography data. Using both simulations and experiments, we show that the multi-plane iterative reconstruction algorithm outperforms the leading multi-plane image sharpening algorithm over a wide range of anisoplantic conditions.

Deep Spectral Reflectance and IlluminantEstimation from Self-Interreflections

Rada DEEB, Joost van de Weijer, Damien Muselet, Mathieu Hébert, and Alain Tremeau

Doc ID: 341923 Received 08 Aug 2018; Accepted 17 Nov 2018; Posted 21 Nov 2018  View: PDF

Abstract: In this work, we propose a CNN-based approach to estimate the spectral reflectance ofa surface and the spectral power distribution of the light from a single RGB image of a V-shapedsurface. Interreflections happening in a concave surface lead to gradients of RGB values overits area. These gradients carry a lot of information concerning the physical properties of thesurface and the illuminant. Our network is trained with only simulated data constructed using aphysics-based interreflection model. Coupling interreflection effects with deep learning helpsto retrieve the spectral reflectance under an unknown light and to estimate the spectral powerdistribution of this light as well. In addition, it is more robust to the presence of image noise thanthe classical approaches. Our results show that the proposed approach outperforms the state ofthe art learning-based approaches on simulated data. In addition, it gives better results on realdata compared to other interreflection-based approaches.

Imaging with two skew ideal lenses

Jakub Belin and Johannes Courtial

Doc ID: 344455 Received 29 Aug 2018; Accepted 23 Oct 2018; Posted 26 Oct 2018  View: PDF

Abstract: In lens systems, the constituent lenses usually share a common optical axis, or at least a common optical-axis direction, and such combinations of lenses are well understood. However, in recent proposals for lens-based transformation-optics devices [Courtial et al., Opt. Express 26, 17872 (2018)] the lenses do not share an optical-axis direction. To facilitate the understanding of such lens systems, we describe here combinations of two ideal lenses in any arbitrary arrangement as a single ideal lens. This description has the potential to become an important tool in understanding novel optical instruments enabled by skew-lens combinations.

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